### Qiaochu Yuan

Shared publicly -Let $latex k$ be a commutative ring and let $latex A$ be a $latex k$-algebra. In this post we’ll investigate a condition on $latex A$ which generalizes the condition that $latex A$ is a finit…

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Qiaochu Yuan

Worked at Machine Intelligence Research Institute

Attends University of California, Berkeley

Lives in Berkeley, CA

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Let $latex k$ be a commutative ring and let $latex A$ be a $latex k$-algebra. In this post we’ll investigate a condition on $latex A$ which generalizes the condition that $latex A$ is a finit…

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Mathematicians are very fond of thinking about algebras. In particular, it’s common to think of commutative algebras as consisting of functions of some sort on spaces of some sort. Less commo…

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Here's a dumb riddle. We all know that a meromorphic function on a Riemann surface is a function to CP^1. We also all know that meromorphic functions on a Riemann surface form a field, and in particular a ring. So... why isn't CP^1 a ring object in the category of Riemann surfaces?

(It took me an embarrassingly long time to figure this out.)

(It took me an embarrassingly long time to figure this out.)

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Is it because the point is not a Riemann surface?

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Once upon a time I imagine people were very happy to think of Lie algebras as "infinitesimal groups," but presumably when infinitesimals fell out of favor this interpretation did too. In this post ...

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Dan Piponi

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You can write code to "implement" a Lie algebra by writing polymorphic code for the group and replacing the base field of reals with the reals extended by infintesimals: http://blog.sigfpe.com/2008/04/infinitesimal-rotations-and-lie.html

The variable I call 'e' gives the comultiplication.

The variable I call 'e' gives the comultiplication.

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Previously we claimed that if you want to check whether a category $latex C$ "behaves like a category of spaces," you can try checking whether it's distributive. The goal of today's post is to just...

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Previously we suggested that if we think of commutative algebras as secretly being functions on some sort of spaces, we should correspondingly think of cocommutative coalgebras as secretly being di…

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Here's a fun question: is the empty function (from the empty set to itself) constant? Is it locally constant?

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Presumably a constant function f:X->Y should factor through pt->Y *uniquely*. If that's the only definition, and X is empty, then "f is constant" iff |Y| = 1. Which is pretty weird!

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Very nice visualization of prime factorizations.

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iirc, this is included in http://incrediblenumbersapp.com/, which is a nice app for kids

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It's common to think of monads as generalized algebraic theories; the most familiar examples, such as the monads on $latex \text{Set}$ encoding groups, rings, and so forth, have this flavor. Howeve...

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Ah, technology. It's a blessing and a curse. To help get more people to read your posts is pure pleasure on my side! In that reign, I tried some categorification-without-looking-at-literature myself, to come up with an alternative to burritos. And these notes want out, if I'd only dare to post them. Maybe more ~~programmers~~ people would like categorification if they knew more...

There. It's promised, nothing can go wrong now. And maybe it even works and someone shows up here for better, or for more.

There. It's promised, nothing can go wrong now. And maybe it even works and someone shows up here for better, or for more.

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Among all of the standard algebraic structures that a student typically encounters in an introduction to abstract algebra (groups, rings, fields, modules), commutative rings are somehow special: th...

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Work

Occupation

Graduate Student

Employment

- Machine Intelligence Research InstituteVisiting Fellow, 2013 - 2013
- PROMYSCounselor, 2012 - 2012
- Stack Overflow, Inc.Intern, 2011 - 2011

Places

Currently

Berkeley, CA

Previously

Boston, MA - New York, NY - Bellevue, WA - Nanjing, China - Singapore - Vancouver, WA - Cambridge, UK

Story

Introduction

I'm a third-year graduate student in mathematics at UC Berkeley.

Bragging rights

USA Mathematical Olympiad Honorable Mention (2006), Siemens-Westinghouse Science and Technology Competition Semifinalist (2007), Intel Science Talent Search Finalist (2008), William Lowell Putnam Mathematical Competition Honorable Mention (2009), NSF Fellow (2012)

Education

- University of California, BerkeleyMathematics, 2012 - present
- Massachusetts Institute of TechnologyMathematics, 2008 - 2012
- University of CambridgeMathematics, 2010 - 2011

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